My degree in math is 10 years old. I was never really "good" at math. It was always hard, a struggle, I missed things, didn't understand pieces, and generally had a rough time of it. The only reason I made it through with a BA in math is persistence and luck.
It is 10 years later and I still think about math a lot.I still wonder about things I missed. I still wish I was "good" at it. Every couple of years, I would pick up a book and try to refresh my knowledge. Then came khanacademy! www.khanacademy.com. It is a great platform for reviewing, filling in the gaps, and proving that you *know* the material. It has gamification makes it fun and makes it clear what you should work on next. You can pick a "mission", be it algebra, geometry, or all of math (mostly High School). It has exercises that are thorough and brutal and change. You don't get through to knowing an exercises until you can do it perfectly 5 times in a row. Once you've gotten through it, you have to "master" it, by doing it again, spaced out in intervals.
I found all sorts of gaps in my knowledge. Things I didn't remember, or never learned. I never really learned how to complete the square, I would always get around it with the quadratic formula. Memorized the volume formulas for 3-dimensional solids? Nope.
So I have been going through it. All of it. From the beginning. 2nd grade. And it is helping me in other areas of my life! It is teaching me how to pay attention, how to read carefully. And I am learning things I never knew and even building up a bit of confidence!
My goal is primarily:
* Get through 90%+ of all the exercises
I recently took a Learning How to Learn course and am going to explain how I am going to apply key things I learned in that course in my quest to win khanacademy. I hope that they will be applicable to other learners, especially older learners going through khanacademy.
Spaced Repetition
Spaced Repetition is a method of getting knowledge from your short-term memory into your long-term memory. It is one of the big things I was missing in my academic life. I would do reasonably well in a class, but months later have nearly forgotten everything I learned.
Khanacademy builds in some spaced repetition via the mastery challenges. Even if you have "mastered" something, a question about it will come up every so often to make sure you remember it. I am also going to add on top of it some flashcards, especially for the things that don't really "stick." If I hit a formula or especially method that seems new, or doesn't immediately stick, I will add it to my new flashcard pile. I am going to apply spaced repetition algorithms similar to Anki's to my deck which will hopefully work for long-term retention.
Recall
When learning new skills, and reviewing old ones, before trying it I try to understand it, then look away and explain it.This was shown to be better that just re-reading it, or just looking at the worked examples.I also try to think through the problems on walks, and see if I can explain it to myself successfully.
Process vs. Product
Focusing on the process instead of the product can be enormously helpful in reducing anxiety and frustration. Sometimes I would get mad that I didn't master a certain skill, or that a grade level was taking too long. Now, instead I just commit to doing 1 25 minute session a day for as long as it takes to get through all the material. In that session, I will do my best to learn and master skills, but I am not going to attach myself to finishing any certain number of skills. I will be using the Pomodoro technique for this!
Exercise
One of the great things I learned in Learning How to Learn was just how crucial exercise is to learning, as was borne out by the research. That is another thing I was definitely missing out on in my academic years. I do exercise pretty often now, but I will commit to doing it more, and realizing more how important it is to learning! It is a great time to live in the "diffuse" mode of learning, and helps our brains process new information better.
Summary
Here is a photo of my progress on all the math skills on khanacademy. I have been working at for about 20-30 minutes a day for over a year. We will see if these new techniques allow me to progress any faster! I hope they can help you through your khanacademy journey as well.
References
A Mind For Numbers (Oakley)
https://www.goodreads.com/book/show/18693655-a-mind-for-numbers?ac=1
Learning How to Learn Coursera Course
https://class.coursera.org/learning-001/
The Pomodoro Technique
http://pomodorotechnique.com/
